Cast on half the number of stitches required plus 1. The extra stitch is required so that you have the correct number of knit stitches after the cast on is complete.
The example shown begins with 21 stitches, for a final 40 stitches.
Join in the round and knit three or four rounds then cut the waste yarn leaving at least a 15cm (6 inch tail).
Join the main yarn and purl two rows. On the last row P2Tog the last two stitches. This will ensure you have the correct number of purls in the final work.
Now those bumps at the bottom are going to be picked up to form knit stitches thus:
Inserting the right needle tip from below knit through the bump, then purl two stitches from the left needle. Pick up two more bumps and knit them, and continue around alternating 2 purls and 2 knits.
After a few rounds of ribbing has been completed, the waste yarn can be removed
And a very stretchy cast on revealed (excuse the strange looking hand)